# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/797435492:0279
# Permalink to this reading: https://leibnizlegible.com/page/797435492:0279?run=74
# Title: [Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ (shelfmarks Leibn. Marg. 0; ZEN Leibn. Marg. 0)
# Folio 59, page id 797435492:0279
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=797435492&page=279
# Source image: https://digitale-sammlungen.gwlb.de/content/797435492/jpgs/default/00000279.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
# Lines: 40 recognised, mean confidence 0.88
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

Y E C T. VIF
DR eodem ordine media inter D L, DL, quo FuerAE I F inter DC.
DE; exume currxe E BF, K B K analo∞X, sEU DExpeTHO D R. DR::
DE. DF.
Nam rurtus D S. + D R. =DI.
DL. +DR. XDI.
DO. + DF. +DE (TunE-.:
DF. +DF. + DF.S
Rurlus, pro circulis alixe linex parallelae, vel analoex substicui
possent.
X. Sine denmuo dux lineae quaeris A OBC, FB F; e altera
FB F CIC ad ictas relata, ux duet a utcunque a detignaro puncto D recta
DC, siF perpetuo D F eodem ordine media proportionalis inter DC,
DE; cum adsumatur linca HI P L. linex A C B analopa (seu ralis, ut
per D uccunque ducta DL S, SINEPErDEtO DS, DL. in eadem ratio-
ne) sic denuo linca R B R calis, ut duet a accunque D L, sit perpetuo
DR eodem ordine media inter DL, DI, quo prius D P inter DC,
DE; erir icidem linca F B F linex R ER analoga.
Rurtus enim DS. + DR + DL. C
DL. +D R +
DC, +D F 
DF. +DF + DF
Cun
Ec ram primi quâr ulcil
mi quatuor cermini
lune proxortionales.
Unde liguer Propoti.
tum.
ZI. Sit Arichmerice proxortionalium Series A. B. C. D, F. F; in
qua sumpris quibuscunque duobus terminis D, P; sc terminorum à
primo A (exclusire) ad ipsum D numerus, N; _ rerminorum ab A
Ciridem exclusire) ad F, lic numerus M; exit A -: D. A: F::
N. M.
am esto differentia communis, Z. eA ergo D = A = NZ. ec
F = A = MX. quarE A --: D = NX. ∞ A - : B = M Z.
unde A-: D. A - : F 3: (NZ. M X:: ) N. M.
XII. Finc, Si duxe fuerinr ejusmodi series; e in uem que lunat
bini,
nde DR. DR33
DE. L